Your understanding of the negative spaces around the objects in a painting will give you a greater feel for its compositional balance. Take it a stage further and consider which regions will be of light, medium and dark tone and have a look to see if it's still balanced.
The identification of negative spaces will allow you to identify which edges of the object need to be hard edges and which could be soft edges i.e. you're identifying those which give you the essence of the image. For example, on the angle-poise lamp the edges of the arm could be soft, because you'd still get the relation between the base and lamp, and the feel for the total object.
Sketching Negative Space
The photo above is of a couple of pages from one of my sketchbooks. The right-hand side of this was also done in the doctor's waiting room (and 'colored in' on a later date). Its origins are in the negative space between the leaves of a huge peace lily. (The single leaf is there as a visual reminder of what kind of plant it was.)
The left-hand page is also a negative-space sketch, this time of the gaps between branches in an oak tree in the garden, done while I was enjoying sitting in the sun.
Using Negative Space for Abstractions
Negative space is also a great starting point for an abstraction, as it takes you a step away from 'reality'. (See How to Paint Abstracts from a Photo.)

